Mistaken Play in the Deferred Acceptance Algorithm: Implications for Positive Assortative Matching

2017 ◽  
Vol 107 (5) ◽  
pp. 225-229 ◽  
Author(s):  
Alex Rees-Jones
Keyword(s):  
Recent Literature ◽  
Welfare Effects ◽  
Assortative Matching ◽  
Welfare Evaluation ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

Recent literature has documented failures of truthful preference reporting in the strategy-proof deferred acceptance algorithm. I consider the implications of these strategic mistakes for a common welfare consideration: the ability of the mechanism to sort the best students to the best schools. I find that these mistakes have the potential to significantly help or significantly hinder sorting. Through this channel, the presence of mistaken play may have widely varying welfare effects. I discuss related considerations in the welfare evaluation of mistaken play in the deferred acceptance algorithm and the implications for “nudges” that correct these mistakes.

scholarly journals Heterogeneous Beliefs and School Choice Mechanisms

2020 ◽  
Vol 110 (5) ◽  
pp. 1274-1315 ◽  
Author(s):  
Adam J. Kapor ◽  
Christopher A. Neilson ◽  
Seth D. Zimmerman
Keyword(s):  
School Choice ◽  
Rational Expectations ◽  
Choice Behavior ◽  
Heterogeneous Beliefs ◽  
Welfare Costs ◽  
Subjective Beliefs ◽  
Opposite Conclusion ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof

This paper studies how welfare outcomes in centralized school choice depend on the assignment mechanism when participants are not fully informed. Using a survey of school choice participants in a strategic setting, we show that beliefs about admissions chances differ from rational expectations values and predict choice behavior. To quantify the welfare costs of belief errors, we estimate a model of school choice that incorporates subjective beliefs. We evaluate the equilibrium effects of switching to a strategy-proof deferred acceptance algorithm, and of improving households’ belief accuracy. We find that a switch to truthful reporting in the DA mechanism offers welfare improvements over the baseline given the belief errors we observe in the data, but that an analyst who assumed families had accurate beliefs would have reached the opposite conclusion. (JEL D83, H75, I21, I28)

scholarly journals The Review of Methods for Assignment of Elective Courses at Universities

2019 ◽  
Vol 57 (4) ◽  
pp. 511-526
Author(s):  
Dejan Trifunović
Keyword(s):  
Business School ◽  
Competitive Equilibrium ◽  
Price Mechanism ◽  
Ex Post ◽  
Elective Courses ◽  
Deferred Acceptance Algorithm ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Pareto Efficient ◽  
Serial Dictatorship

AbstractIn this paper we present a review of matching algorithms that are used for matching students with elective courses at universities. This is an example of a market where price mechanism cannot be used to determine the equilibrium allocation. In the Random Serial Dictatorship students select courses based on their position in a random queue. This mechanism is not ex post Pareto-efficient and its drawback is overcome in the Probabilistic Serial Assignment, although this mechanism is not strategy-proof. In the auction mechanism, students’ bids for courses do not represent their true preferences, since bids depend on their beliefs about the popularity of courses. The efficient allocation is obtained when Deferred Acceptance Algorithm is used - where the priority of students is determined based on their bids. Harvard draft mechanism is based on changing the order of students in the random queue from one round to another and this mechanism is not strategy-proof; however, it is, by all means, better for students than Random Serial Dictatorship. The Wharton Business School mechanism is based on the calculation of approximate competitive equilibrium.

scholarly journals The Welfare Effects of Coordinated Assignment: Evidence from the New York City High School Match

2017 ◽  
Vol 107 (12) ◽  
pp. 3635-3689 ◽  
Author(s):  
Atila Abdulkadiroğlu ◽  
Nikhil Agarwal ◽  
Parag A. Pathak
Keyword(s):  
High School ◽  
New York ◽  
New York City ◽  
Education Reform ◽  
York City ◽  
Popular Education ◽  
Welfare Effects ◽  
Student Preferences ◽  
Deferred Acceptance ◽  
School Assignment

Coordinated single-offer school assignment systems are a popular education reform. We show that uncoordinated offers in NYC's school assignment mechanism generated mismatches. One-third of applicants were unassigned after the main round and later administratively placed at less desirable schools. We evaluate the effects of the new coordinated mechanism based on deferred acceptance using estimated student preferences. The new mechanism achieves 80 percent of the possible gains from a no-choice neighborhood extreme to a utilitarian benchmark. Coordinating offers dominates the effects of further algorithm modifications. Students most likely to be previously administratively assigned experienced the largest gains in welfare and subsequent achievement. (JEL C78, D82, I21, I28)

scholarly journals Beyond Truth-Telling: Preference Estimation with Centralized School Choice and College Admissions

2019 ◽  
Vol 109 (4) ◽  
pp. 1486-1529 ◽  
Author(s):  
Gabrielle Fack ◽  
Julien Grenet ◽  
Yinghua He
Keyword(s):  
School Choice ◽  
Test Scores ◽  
Real Life ◽  
Truth Telling ◽  
Student Preferences ◽  
Ex Post ◽  
Is Strategy ◽  
Deferred Acceptance ◽  
Strategy Proof ◽  
Novel Approaches

We propose novel approaches to estimating student preferences with data from matching mechanisms, especially the Gale-Shapley deferred acceptance. Even if the mechanism is strategy-proof, assuming that students truthfully rank schools in applications may be restrictive. We show that when students are ranked strictly by some ex ante known priority index (e.g., test scores), stability is a plausible and weaker assumption, implying that every student is matched with her favorite school/college among those she qualifies for ex post. The methods are illustrated in simulations and applied to school choice in Paris. We discuss when each approach is more appropriate in real-life settings. (JEL D11, D12, D82, I23)

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